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Mean squared displacement in a generalized Lévy walk model.

M Bothe1, F Sagues2, I M Sokolov3

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This study investigates a generalized Lévy walk model, revealing its mean squared displacement (MSD) behavior mirrors the original model where it exists. It clarifies conditions for MSD existence or divergence in turbulent dispersion models.

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Area of Science:

  • Stochastic processes
  • Statistical physics
  • Turbulence modeling

Background:

  • Lévy walks are stochastic models with diverse applications.
  • The Richardson law describes turbulent dispersion.
  • Previous work challenged the Richardson regime in original Lévy walk models due to MSD divergence.

Purpose of the Study:

  • Investigate a generalized Lévy walk model.
  • Analyze the mean squared displacement (MSD) behavior.
  • Determine conditions for MSD existence or divergence.

Main Methods:

  • Detailed investigation of ensemble MSD.
  • Comparison with the original Lévy walk model.
  • Analysis of ordinary and aged situations.

Main Results:

  • The generalized model's MSD behavior matches the original model where it exists.
  • Identified conditions under which the MSD exists or diverges.
  • The generalized model interpolates between original and Drude-like models.

Conclusions:

  • The generalized Lévy walk model provides a more robust framework for studying phenomena like turbulent dispersion.
  • Understanding MSD behavior is crucial for accurate modeling of physical processes.
  • This work resolves ambiguities regarding the Richardson regime in Lévy walk models.